MCMC-Correction of Score-Based Diffusion Models for Model Composition

• URL: http://arxiv.org/abs/2307.14012v3
• Date: Thu, 05 Jun 2025 19:27:06 GMT
• Title: MCMC-Correction of Score-Based Diffusion Models for Model Composition
• Authors: Anders Sjöberg, Jakob Lindqvist, Magnus Önnheim, Mats Jirstrand, Lennart Svensson,
• Abstract summary: Diffusion models can be parameterized in terms of a score or an energy function.<n>We introduce a novel MH-like acceptance rule based on line integration of the score function.
• Score: 2.682859657520006
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models can be parameterized in terms of either a score or an energy function. The energy parameterization is attractive as it enables sampling procedures such as Markov Chain Monte Carlo (MCMC) that incorporates a Metropolis-Hastings (MH) correction step based on energy differences between proposed samples. Such corrections can significantly improve sampling quality, particularly in the context of model composition, where pre-trained models are combined to generate samples from novel distributions. Score-based diffusion models, on the other hand, are more widely adopted and come with a rich ecosystem of pre-trained models. However, they do not, in general, define an underlying energy function, making MH-based sampling inapplicable. In this work, we address this limitation by retaining the score parameterization and introducing a novel MH-like acceptance rule based on line integration of the score function. This allows the reuse of existing diffusion models while still combining the reverse process with various MCMC techniques, viewed as an instance of annealed MCMC. Through experiments on synthetic and real-world data, we show that our MH-like samplers offer comparable improvements to those obtained with energy-based models, without requiring explicit energy parameterization.

Related papers

• Multi-fidelity Parameter Estimation Using Conditional Diffusion Models [6.934199382834925]
  We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems. We use conditional generative models trained to sample the target conditional distribution. We demonstrate the effectiveness of the proposed method on several numerical examples.
  arXiv  Detail & Related papers  (2025-04-02T16:54:47Z)
• Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo [18.377963220078442]
  We introduce a novel training regime for the energy function through distillation of pre-trained diffusion models. We showcase the synergies between energy and score by casting the diffusion sampling procedure as a Feynman Kac model.
  arXiv  Detail & Related papers  (2025-02-18T11:47:44Z)
• Energy-Based Diffusion Language Models for Text Generation [126.23425882687195]
  Energy-based Diffusion Language Model (EDLM) is an energy-based model operating at the full sequence level for each diffusion step. Our framework offers a 1.3$times$ sampling speedup over existing diffusion models.
  arXiv  Detail & Related papers  (2024-10-28T17:25:56Z)
• EM Distillation for One-step Diffusion Models [65.57766773137068]
  We propose a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of quality. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process.
  arXiv  Detail & Related papers  (2024-05-27T05:55:22Z)
• Adaptive Fuzzy C-Means with Graph Embedding [84.47075244116782]
  Fuzzy clustering algorithms can be roughly categorized into two main groups: Fuzzy C-Means (FCM) based methods and mixture model based methods. We propose a novel FCM based clustering model that is capable of automatically learning an appropriate membership degree hyper- parameter value.
  arXiv  Detail & Related papers  (2024-05-22T08:15:50Z)
• Iterated Denoising Energy Matching for Sampling from Boltzmann Densities [109.23137009609519]
  Iterated Denoising Energy Matching (iDEM) iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our matching objective. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5times$ faster.
  arXiv  Detail & Related papers  (2024-02-09T01:11:23Z)
• Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learning [13.22531381403974]
  Generalized Contrastive Divergence (GCD) is a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. We present preliminary yet promising results showing that joint training is beneficial for both EBM and a diffusion model.
  arXiv  Detail & Related papers  (2023-12-06T10:10:21Z)
• Learning Energy-Based Prior Model with Diffusion-Amortized MCMC [89.95629196907082]
  Common practice of learning latent space EBMs with non-convergent short-run MCMC for prior and posterior sampling is hindering the model from further progress. We introduce a simple but effective diffusion-based amortization method for long-run MCMC sampling and develop a novel learning algorithm for the latent space EBM based on it.
  arXiv  Detail & Related papers  (2023-10-05T00:23:34Z)
• Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood [64.95663299945171]
  Training energy-based models (EBMs) on high-dimensional data can be both challenging and time-consuming. There exists a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. We propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs.
  arXiv  Detail & Related papers  (2023-09-10T22:05:24Z)
• Accelerating Markov Chain Monte Carlo sampling with diffusion models [0.0]
  We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a Metropolis-Hastings algorithm with a diffusion model. We briefly review diffusion models in the context of image synthesis before providing a streamlined diffusion model tailored towards low-dimensional data arrays. Our approach leads to a significant reduction in the number of likelihood evaluations required to obtain an accurate representation of the posterior.
  arXiv  Detail & Related papers  (2023-09-04T09:03:41Z)
• Conservative objective models are a special kind of contrastive divergence-based energy model [5.02384186664815]
  We show thatCOMs for offline model-based optimisation are a special kind of contrastive divergence-based energy model. We show that better samples can be obtained if the model is decoupled so that the unconditional and conditional probabilities are modelled separately.
  arXiv  Detail & Related papers  (2023-04-07T23:37:50Z)
• Particle Dynamics for Learning EBMs [83.59335980576637]
  Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation of samples from the current energy function at each iteration. This paper proposes an alternative approach to getting these samples and avoiding crude MCMC sampling from the current model.
  arXiv  Detail & Related papers  (2021-11-26T23:41:07Z)
• Oops I Took A Gradient: Scalable Sampling for Discrete Distributions [53.3142984019796]
  We show that this approach outperforms generic samplers in a number of difficult settings. We also demonstrate the use of our improved sampler for training deep energy-based models on high dimensional discrete data.
  arXiv  Detail & Related papers  (2021-02-08T20:08:50Z)
• Learning Energy-Based Model with Variational Auto-Encoder as Amortized Sampler [35.80109055748496]
  Training energy-based models (EBMs) by maximum likelihood requires Markov chain Monte Carlo sampling. We learn a variational auto-encoder (VAE) to initialize the finite-step MCMC, such as Langevin dynamics that is derived from the energy function. With these amortized MCMC samples, the EBM can be trained by maximum likelihood, which follows an "analysis by synthesis" scheme. We call this joint training algorithm the variational MCMC teaching, in which the VAE chases the EBM toward data distribution.
  arXiv  Detail & Related papers  (2020-12-29T20:46:40Z)
• Semi-nonparametric Latent Class Choice Model with a Flexible Class Membership Component: A Mixture Model Approach [6.509758931804479]
  The proposed model formulates the latent classes using mixture models as an alternative approach to the traditional random utility specification. Results show that mixture models improve the overall performance of latent class choice models.
  arXiv  Detail & Related papers  (2020-07-06T13:19:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.